Construction of discrete series representations of SOe(4,1) via algebraic Dirac induction

Abstract

The notion of algebraic Dirac induction was introduced by P. Pandžić and D. Renard. This is a construction which gives representations with prescribed Dirac cohomology. They proved that all holomorphic discrete series representations can be constructed via Dirac induction. All discrete series representations of the group $S{O}_e(4,1)$ are nonholomorphic. In this paper we prove that they can also be constructed using algebraic Dirac induction.

Communicated by Silvana Bazzoni

Keywords:

• Dirac cohomology
• Dirac induction
• discrete series

2010 Mathematics Subject Classification:

• Primary: 22E47
• Secondary: 22E46

Acknowledgments

The author is grateful to Pavle Pandžić for a careful reading of the paper and his comments.

Additional information

Funding

The author is supported by the QuantiXLie Centre of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund – the Competitiveness and Cohesion Operational Programme (Grant KK.01.1.1.01.0004).